Let me work through this payroll case.

Inputs:
- Payroll record: gross_pay = 4999.99, payroll_month = 2026-02, allowed_deduction = 264.22
- Contract: gross_pay = 5019.61
- Amendment: gross_pay = 4999.99, approved = true, effective_month = 2026-01
- Case reference schedule: first-half: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3300.00, middle_rate 0.08, upper_rate 0.18; second-half: rate 0.08, cap 3500.00, deduction 400.00, free 1000.00, upper 3000.00, middle_rate 0.14, upper_rate 0.24

Step 1: Check R7 order.
1. gross_pay present: 4999.99. OK.
2. payroll_month present: 2026-02. OK.
3. Reference row: 2026-02 is in first-half (2026-01 through 2026-06). Use the case schedule's first-half row (per R1, the schedule replaces defaults).
4. Contract conflict: contract gross_pay = 5019.61 differs from payroll gross_pay = 4999.99. Check amendment under R9: approved = true, effective_month = 2026-01 ≤ 2026-02, amount = 4999.99 equals payroll record's gross_pay = 4999.99. So the amendment resolves the conflict. Proceed with gross_pay = 4999.99. Cite R9.

Step 2: Employee contribution (R3).
Rate = 0.07 (first-half schedule). Wage cap = 5000.00.
min(4999.99, 5000.00) = 4999.99.
Contribution = 0.07 × 4999.99 = 349.9993. Round to two decimals: 350.00 (round-half-up: 349.9993 → 350.00).

Wait: 349.9993 rounded to two decimals: the third decimal is 9, so 349.9993 → 350.00? Let's check: 349.9993. Two decimal places: 349.99|93. The digits after are 93, which is ≥ 50, so round up: 349.99 + 0.01 = 350.00. Yes, 350.00.

Step 3: Allowed deduction (R4).
allowed_deduction = 264.22. Cap = 400.00 (schedule). Gross pay minus rounded contribution = 4999.99 − 350.00 = 4649.99. 264.22 ≤ 400.00 and ≤ 4649.99. OK.

Step 4: Taxable pay (R4).
Taxable = 4999.99 − 350.00 − 264.22 = 4385.77.

Check: 4999.99 − 350.00 = 4649.99. 4649.99 − 264.22 = 4385.77. Yes.

Step 5: Income tax (R5).
First-half schedule: free = 900.00, upper = 3300.00, middle_rate = 0.08, upper_rate = 0.18.

Taxable = 4385.77.
- Portion up to 900.00: untaxed.
- Portion 900.00 to 3300.00: 3300.00 − 900.00 = 2400.00 at 0.08 = 192.00.
- Portion above 3300.00: 4385.77 − 3300.00 = 1085.77 at 0.18 = 195.4386.

Total = 192.00 + 195.4386 = 387.4386. Round to 387.44.

Step 6: Net pay (R6).
Net = 4999.99 − 350.00 − 264.22 − 387.44 = ?

4999.99 − 350.00 = 4649.99.
4649.99 − 264.22 = 4385.77.
4385.77 − 387.44 = 3998.33.

Net pay = 3998.33.

Answer fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4999.99"
- employee_contribution: "350.00"
- allowed_deduction: "264.22"
- taxable_pay: "4385.77"
- income_tax: "387.44"
- net_pay: "3998.33"
- clauses: R1 (row selection + schedule), R9 (amendment resolving conflict), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay).

Per the rules: "Calculated answers cite R1 through R6, and also R9 only when an amendment is needed to resolve a conflict." Here the amendment is needed because contract differs. So include R9.

Clauses: ["R1", "R2", "R3", "R4", "R5", "R6", "R9"].

Should I include an explanation? Optional. I can add a brief explanation noting the amendment resolved the conflict and the schedule row used. Keep it concise.

Money as strings with two decimals. No markdown fences. One JSON object.

Let me double-check the tax computation without rounding intermediate products: 
- Middle band: 2400.00 × 0.08 = 192.00
- Upper band: 1085.77 × 0.18 = 195.4386
Sum = 387.4386 → 387.44. Correct.

Contribution: 4999.99 × 0.07 = 349.9993 → 350.00. Correct.

Net: 3998.33. Verify: gross − contribution − deduction − tax = 4999.99 − 350.00 − 264.22 − 387.44.
4999.99 − 350.00 = 4649.99
4649.99 − 264.22 = 4385.77
4385.77 − 387.44 = 3998.33. Correct.

Output JSON.

Let me work through this payroll calculation.

Inputs:
- Payroll record: gross_pay = 4999.99, payroll_month = 2026-02, allowed_deduction = 264.22
- Contract: gross_pay = 5019.61
- Amendment: gross_pay = 4999.99, approved = true, effective_month = 2026-01
- Case reference schedule (authoritative):
  - first-half: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3300.00, middle_rate 0.08, upper_rate 0.18
  - second-half: rate 0.08, cap 3500.00, deduction 400.00, free 1000.00, upper 3000.00, middle_rate 0.14, upper_rate 0.24

Step 1: Check conflicts (R7 order):
1. gross_pay present: 4999.99 ✓
2. payroll_month present: 2026-02 ✓
3. 2026-02 is covered (first-half row, but the case schedule replaces defaults). ✓
4. contract_gross_pay = 5019.61 differs from gross_pay = 4999.99. Check amendment: approved = true, effective_month = 2026-01 ≤ 2026-02, amendment gross_pay = 4999.99 equals payroll record gross_pay = 4999.99. So the amendment resolves the conflict under R9. Calculation proceeds, citing R9 as well.

Step 2: Select reference row. Payroll month 2026-02 → first-half row. Case schedule first-half: rate 0.07, cap 5000.00, deduction cap 400.00, free 900.00, upper 3300.00, middle 0.08, upper rate 0.18.

Step 3: Employee contribution (R3): rate × min(gross, cap) = 0.07 × min(4999.99, 5000.00) = 0.07 × 4999.99 = 349.9993. Round to two decimals half-up: 350.00.

Wait, 0.07 × 4999.99 = 349.9993. Rounded: 350.00.

Step 4: Allowed deduction check (R4): allowed_deduction = 264.22. Must not exceed deduction cap (400.00) or gross pay minus rounded contribution = 4999.99 − 350.00 = 4649.99. 264.22 ≤ both. OK.

Step 5: Taxable pay (R4): gross − contribution − deduction = 4999.99 − 350.00 − 264.22 = 4385.77.

Step 6: Income tax (R5), first-half schedule: free = 900.00, upper boundary = 3300.00, middle_rate = 0.08, upper_rate = 0.18.

- Portion up to 900: untaxed.
- Portion 900 to 3300: 3300 − 900 = 2400 at 0.08 = 192.00.
- Portion above 3300: 4385.77 − 3300 = 1085.77 at 0.18 = 195.4386.

Total tax = 192.00 + 195.4386 = 387.4386 → round half-up to 387.44.

Step 7: Net pay (R6): gross − contribution − deduction − tax = 4999.99 − 350.00 − 264.22 − 387.44 = 3998.33.

Let me verify: 4999.99 − 350.00 = 4649.99. 4649.99 − 264.22 = 4385.77. 4385.77 − 387.44 = 3998.33. ✓

Answer fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4999.99"
- employee_contribution: "350.00"
- allowed_deduction: "264.22"
- taxable_pay: "4385.77"
- income_tax: "387.44"
- net_pay: "3998.33"
- clauses: R1, R2, R3, R4, R5, R6, R9 (amendment needed to resolve conflict)

Citations: "Calculated answers cite R1 through R6, and also R9 only when an amendment is needed to resolve a conflict." Here the amendment was needed (contract differs), so include R9.

The case schedule replaces defaults — R1 covers that. Should I cite R1? Yes, R1 covers row selection and schedule authority.

Output JSON without markdown fences, one object. Allowed fields plus optional explanation. I'll include a brief explanation noting the amendment resolved the conflict.

Check tax computation precision: 0.08 × 2400 = 192.00 exactly. 0.18 × 1085.77 = 195.4386. Sum = 387.4386 → 387.44 (round half up at two decimals: 387.4386 → third decimal is 8... wait, 387.4386, two decimals: 387.43|86 → rounds to 387.44). Yes.

Net pay check again: 4999.99 − 350.00 − 264.22 − 387.44 = 3998.33. ✓

Let me work through this payroll record.

Inputs:
- gross_pay: 4999.99
- payroll_month: 2026-02
- allowed_deduction: 264.22
- contract gross_pay: 5019.61
- amendment: gross_pay 4999.99, approved: true, effective_month: 2026-01

First, check R7 order:
1. gross_pay present: 4999.99 ✓
2. payroll_month present: 2026-02 ✓
3. Reference row: 2026-02 is in 2026-01 through 2026-06 → first-half. But there's an authoritative case reference schedule. The schedule's first-half row: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3300.00, middle_rate 0.08, upper_rate 0.18. This replaces defaults.
4. Contract conflict: contract gross_pay 5019.61 differs from payroll gross_pay 4999.99. Amendment: approved true, effective_month 2026-01 ≤ 2026-02, amount 4999.99 equals payroll record gross_pay 4999.99. So the amendment resolves the conflict under R9. Cite R9 in addition to R1–R6.

Now calculate:

Employee contribution (R3): rate 0.07 × min(4999.99, 5000.00) = 0.07 × 4999.99 = 349.9993 → round to 350.00 (round-half-up). 0.07 × 4999.99 = 349.9993. Round to two decimals: 350.00? 349.9993 rounds to 350.00 (since third decimal is 9, we round up: 349.9993 → 350.00). Wait, 349.9993 to two decimals: look at 349.9993, the third decimal is 9 (349.99|93), so rounding 349.99 + 0.0093 → rounds to 350.00. Yes, 350.00.

Allowed deduction (R4): 264.22. Check: must not exceed deduction cap 400.00 (schedule) ✓, and must not exceed gross pay minus rounded contribution: 4999.99 − 350.00 = 4649.99. 264.22 ≤ 4649.99 ✓.

Taxable pay (R4): gross − contribution − deduction = 4999.99 − 350.00 − 264.22 = 4385.77.

Income tax (R5): brackets from schedule: free 900.00, upper 3300.00, middle_rate 0.08, upper_rate 0.18.
- Portion up to 900: 0 tax.
- Portion 900 to 3300: 2400.00 × 0.08 = 192.00.
- Portion above 3300: 4385.77 − 3300.00 = 1085.77 × 0.18 = 195.4386.
Total tax = 192.00 + 195.4386 = 387.4386 → round to 387.44.

Net pay (R6): 4999.99 − 350.00 − 264.22 − 387.44 = ?
4999.99 − 350.00 = 4649.99
4649.99 − 264.22 = 4385.77
4385.77 − 387.44 = 3998.33.

Net pay = 3998.33.

Answer fields: decision "calculate", currency "LCR", gross_pay "4999.99", employee_contribution "350.00", allowed_deduction "264.22", taxable_pay "4385.77", income_tax "387.44", net_pay "3998.33".

Clauses: R1, R2, R3, R4, R5, R6, R9 (amendment needed to resolve conflict).

Let me double-check the contribution: 0.07 × 4999.99 = 349.9993. Rounded half-up to two decimals: 350.00. Yes.

Taxable pay: 4999.99 − 350.00 − 264.22 = 4385.77. Yes.

Tax: (3300 − 900) = 2400 × 0.08 = 192.00. (4385.77 − 3300) = 1085.77 × 0.18 = 195.4386. Sum = 387.4386 → 387.44.

Net: 4385.77 − 387.44 = 3998.33.

Note: do not include input-only fields like contract_gross_pay or amendment. Include optional explanation maybe.

JSON output without markdown fences.